Mathematical model of errors in measuring the interframe displacement of a measuring mark on an observation object using video from a WEB camera
This paper develops and analyses a mathematical error model for estimating the potential accuracy of measuring the inter‑frame displacement of a reference marker captured by a WEB camera. The case is considered when the WEB video camera is installed at a distance of about tens of centimeters from th...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Zhytomyr Polytechnic State University
2025-07-01
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| Series: | Технічна інженерія |
| Subjects: | |
| Online Access: | https://ten.ztu.edu.ua/article/view/334981 |
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| Summary: | This paper develops and analyses a mathematical error model for estimating the potential accuracy of measuring the inter‑frame displacement of a reference marker captured by a WEB camera. The case is considered when the WEB video camera is installed at a distance of about tens of centimeters from the measuring mark. The tag is the limb of the rotary mechanism of the ground antenna system of the X-band space radio link. Marker shift between consecutive video frames is calculated by locating the peak of the cross‑correlation function computed along corresponding image rows; this shift is then recalculated into antenna angle variation.
Expressions link the root‑mean‑square (RMS) displacement error to observation conditions. For low‑cost webcams, the maximum admissible pixel illumination and the RMS sensor noise-voltage values absent from manufacturer data are obtained through an original estimation procedure.
The paper also evaluates inter‑row signal accumulation for a marker consisting of vertical ticks of scale and shows that, under adequate artificial lighting, such accumulation is counter‑productive because it leads to the increase of the mean value of matrix‑fluctuation noise.
For a discussed case for a cheap webcam-calculated potential antenna, the rotation error is of ≈ 0.2 arc‑seconds. Air turbulence, mechanical vibration, drivetrain inaccuracies and spectral mismatches were not discussed in the present scope. The model and guidelines can be of value for designers of opto‑electronic, non‑contact position‑measurement systems. |
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| ISSN: | 2706-5847 2707-9619 |